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ex1 - EE 6331 – Spring 2010 – Sample Exam 1 1 Consider...

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Unformatted text preview: EE 6331 – Spring 2010 – Sample Exam 1 1. Consider a system described by the input output model 3 2 (a) Find the transfer function G(s) (b) Find a state space representation in companion form 2 2. Consider two state equations ̅ Where 4 1 3 , 0 1 , 0 1, 4 ̅ 3 2 1 , 0 1̅ , 1 1, 0 (a) Are the two state equations equivalent? (b) Are the two state equations zero state equivalent? (c) What are the matrix 1,2 and -norms of A and ̅? What are the vector 1,2 and -norms of B and ? 3. Consider the LTI system 0 1 2, 1 A is a 2x2 matrix with eigenvalues -2 and -3 and corresponding eigenvectors 2 2 , 1 2 (a) Find A (b) Using two methods, find (c) If u(t)=0 for all t, what (if anything) can be said about y(t) as ? 2 0 4. Consider the nonlinear system cos 4 (if equilibrium points are (a) Suppose u=0 is the input. Find the equilibrium states repeated at regular intervals, just find the first instance and state how often it is repeated) (b) Linearize the system about each equilibrium state, include input u (c) Compute the transfer function G(s) of the linearized system at each equilibrium state ...
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